The former Derby County player has fallen out of the first team picture at St Mary's with Claus Lundekvam and Michael Svensson becoming the regular central defensive pairing and new signing Fitz Hall arriving as back-up.
Tony Pulis has declared his intentions to strengthen his Stoke squad and the signing of Williams would add some much needed experience to help his young team.
Gordon Strachan has signed the 32-year old in his spells in charge of Southampton and Coventry City but may let the player leave in order for him to get the chance of regular action.
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